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JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant

Let \(A\) be a \(3\times3\) matrix such that \(A\left[ {\begin{array}{*{20}{c}}
  1&2&3 \\ 
  0&2&3 \\ 
  0&1&1 
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
  0&0&1 \\ 
  1&0&0 \\ 
  0&1&0 
\end{array}} \right]\)  Then \(A^{-1}\) is

  1. A \(\left[ {\begin{array}{*{20}{c}}
      3&1&2 \\ 
      3&0&2 \\ 
      1&0&1 
    \end{array}} \right]\)
  2. B \(\left[ {\begin{array}{*{20}{c}}
      3&2&1 \\ 
      3&2&0 \\ 
      1&1&0 
    \end{array}} \right]\)
  3. C \(\left[ {\begin{array}{*{20}{c}}
      0&1&3 \\ 
      0&2&3 \\ 
      1&1&1 
    \end{array}} \right]\)
  4. D \(\left[ {\begin{array}{*{20}{c}}
      1&2&3 \\ 
      0&1&1 \\ 
      0&2&3 
    \end{array}} \right]\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\left[ {\begin{array}{*{20}{c}}
  3&1&2 \\ 
  3&0&2 \\ 
  1&0&1 
\end{array}} \right]\)

Step-by-step Solution

Detailed explanation

Given \(A\left[ {\begin{array}{*{20}{c}} 1&2&3\\ 0&2&3\\ 0&1&1 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 0&0&1\\ 1&0&0\\ 0&1&0 \end{array}} \right]\) Applying \({C_1} \leftrightarrow {C_3}\)…